|
Search: id:A001785
|
|
|
| A001785 |
|
Second order reciprocal Stirling number (Fekete) [[2n+4, n]]. The number of n-orbit permutations of a (2n+4)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g. Comtet).
(Formerly M5382 N2338)
|
|
+0
4
|
|
| 1, 120, 7308, 303660, 11098780, 389449060, 13642629000, 486591585480, 17856935296200, 678103775949600, 26726282654771700, 1094862336960892500, 46641683693715610500, 2066075391660447667500, 95122549872697437090000
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
A. E. Fekete, Apropos two notes on notation, Amer. Math. Monthly, 101 (1994), 771-778.
C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.
|
|
FORMULA
|
[[2n+4, n]]=sum((-1)^i*binomial(2n+4, 2n+4-i)[2n+4-i, n-i] where [n, k] is the unsigned Stirling number of the first kind.
|
|
MAPLE
|
with(combinat):s1 := (n, k)->sum((-1)^i*binomial(n, i)*abs(stirling1(n-i, k-i)), i=0..n); for j from 1 to 20 do s1(2*j+4, j); od;
|
|
CROSSREFS
|
Cf. A000907, A000483, A001784.
Sequence in context: A055213 A035190 A035815 this_sequence A076005 A104592 A135379
Adjacent sequences: A001782 A001783 A001784 this_sequence A001786 A001787 A001788
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms, Maple program, formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Dec 14 2000
|
|
|
Search completed in 0.002 seconds
|
